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JEE Main 2010
Exam
JEE Main
Year
2010
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2010 · Mathematics · Area Under Curves

The area bounded by the curves y= x and y= x between the ordinates...

The area bounded by the curves y=cos⁡xy=\cos x and y=sin⁡xy=\sin x between the ordinates x=0x=0 and x=3π2x=\frac{3 \pi}{2} isThe area bounded by the curves y= x and y= x between the ordinates x=0 and x=(3 π)/(2) is

Options

  1. A42+24 \sqrt{2}+2
  2. B42−14 \sqrt{2}-1
  3. C42+14 \sqrt{2}+1
  4. D42−24 \sqrt{2}-2

Correct answer

D. 42−24 \sqrt{2}-2

Step-by-step solution

∫0π4(cos⁡x−sin⁡x)dx+∫π45π4(sin⁡x−cos⁡x)dx+∫5π43π2(cos⁡x−sin⁡x)=42−2\int_0^{\frac{\pi}{4}}(\cos x-\sin x) d x+\int_{\frac{\pi}{4}}^{\frac{5 \pi}{4}}(\sin x-\cos x) d x+\int_{\frac{5 \pi}{4}}^{\frac{3 \pi}{2}}(\cos x-\sin x)=4 \sqrt{2}-2 The area bounded by the curves y= x and y= x between the ordinates x=0 and x=(3 π)/(2) is
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